Shared autonomous vehicles (SAVs) are expected to enhance urban transportation efficiency through innovative mobility resource management. By developing a comprehensive agent-based simulation framework, this study investigates several key factors influencing fleet size and parking demand for the adoption of SAVs in future urban mobility systems. The framework evaluates how both operational factors (e.g., reservation time and maximum waiting time) and demand-side characteristics (e.g., demand rate and the balance between trip origins and destinations) jointly affect the performance of the SAV system. It uses a two-stage simulation process that includes capacity estimation and performance evaluation. In the initial warm-up stage, the simulation estimates the fleet size and parking spaces needed to serve specific travel demand. These initial estimates are then used in the second stage to run further simulations and assess additional performance indicators, including final required parking spaces, empty meters traveled, and trip rejection rate. To obtain a holistic understanding of the studied factors, we construct various simulation scenarios based on historical taxi data in central areas of Chengdu, Shanghai (China), and Manhattan of New York City (USA), and build structural regression models on the simulation outcomes. The results reveal a general mechanism by which operational characteristics and demand patterns influence SAV fleet and parking sizes. We find that a 1 % increase in overall travel demand results in about a 1 % increase in the number of SAVs needed and required parking spaces. Meanwhile, a 1 % improvement in the balance of origin-destination (OD) trips, which reduces spatial mismatches between vehicle supply and trip requests, can help offset the need for additional vehicles and parking spaces. These findings offer critical policy implications, emphasizing the need for integrating SAV deployment with land-use strategies, balancing fleet investment, environmental costs, and service quality (e.g., lower waiting time) in SAV planning and operations.